Related papers: Canonical transformations and squeezing formalism …
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
We report here the status of different gauge conditions in the canonical formulation of quantum electrodynamics on light-front surfaces. We start with the massive vector fields as pedagogical models where all basic concepts and possible…
We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard…
In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…
The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and…
By efforts of several authors, it is recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated in terms of that in the long wavelength limit, and the latter can be…
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in…